Which of the following inequalities is graphed on the coordinate plane?

C

Because the graph of the line is y = 2x + 2

The graph is shaded above the line, so we want y values above the line and since it is shaded in (red and not dashed), we want the values above and on the line (aka greater than or equal to SIGN)

C. y≥2x+2

Step-by-step explanation:

We have that the line plotted in the graph is y=2x+2.

Now, we see that, the plotted line is not a dotted line, so the inequality will include the equality.

i.e. either y≥2x+2 or y≤2x+2.

As, we see that the solution region in the graph is away from the origin.

And, Zero test states that after substituting the point (0,0) in the inequality. If the result is true, the solution region is graphed towards the origin. If the result is false,the solution region is graphed away from the origin.

So, we put (0,0) in the possible options, we get,

y≥2x+2 ⇒ 0 ≥ 2, which is false and  y≤2x+2 ⇒ 0 ≤ 2, which is true.

So, we get, y≥2x+2 will have the solution region graphed away from the origin.

Hence, option C is correct.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

x+14

step-by-step explanation: